# How do you factor y^2-16+64?

Jan 24, 2016

This trinomial is a perfect square trinomial, so can be factored as ${\left(a - b\right)}^{2}$

#### Explanation:

The square root of 64 is 8 and the square root of ${y}^{2}$ is y.

The middle term should be of the form 2ab. In this case, a=y and b= 8

So, 2(y)(8), or 16y, which is the middle term. This short proof justifies that it is indeed a perfect square trinomial.

${y}^{2}$ - 16y + 64
= (y - 8)(y - 8)
= ${\left(y - 8\right)}^{2}$

Your answer is ${\left(y - 8\right)}^{2}$

Exercises:

1. Out of the following trinomials, which is/are perfect square trinomial(s)?

a). ${y}^{2}$ - 16

B) ${y}^{2}$ + 8y + 16

C) ${y}^{2}$ + 16

D) ${y}^{2}$ - 8y + 16

1. Factor the following perfect square trinomial:

$4 {x}^{2}$ + 28x + 49

Hopefully you understand now!